"Matthew makes me proud because he is very humble and sincere and a very thoughtful person," she tells PEOPLE. "He is just a great son."

Not to mention a natural family man. As husband to Camila, 31, and father to their kids Levi, 5½, Vida, 4, and 15-month-old Livingston, Matthew, 44, couldn't have had a better role model than his own dad, James, a gas-station owner who died in 1992, says Kay.

"I had no doubt when he decided to marry, which he took his time doing, that he would be a thoughtful, trustful husband," says Kay, 82, a former schoolteacher. As for Matthew being a father, "Well, he was brought up seeing his dad show these traits, and setting a good example is always the best teacher," Kay adds.

"Matthew was always gearing up to be a great dad. He loved his dad so much, and he lost him early," says Linklater, a close friend who directed McConaughey in his first movie, Dazed and Confused, and in The Newton Boys and Bernie. "I just always knew he'd be a really special father."

And as long as they're all together, adds Linklater, life is good for the McConaughey brood. "Those kids are living a pretty adventurous life right out of the gate," he says. "The kids go where they go. They're never going to be bored. It's awesome!"

For much more on McConaughey's journey – and a closer look at his evolution from Texas teen to romantic comedy king to Oscar champ – pick up this week's issue of PEOPLE.